Problem: $f(x) = \dfrac{ x + 7 }{ ( x + 7 )( x - 4 ) }$ What is the domain of the real-valued function $f(x)$ ?
Answer: $f(x)$ is undefined when the denominator is 0. The denominator is 0 when $x=-7$ or $x=4$ So we know that $x \neq -7$ and $x \neq 4$ Expressing this mathematically, the domain is $\{ \, x \in \RR \mid x \neq-7, \,x \neq4\, \}$.